let X be BCI-algebra; :: thesis: ( ( for X being BCI-algebra

for x, y being Element of X holds x \ (y \ x) = x ) implies the carrier of X = BCK-part X )

assume for X being BCI-algebra

for x, y being Element of X holds x \ (y \ x) = x ; :: thesis: the carrier of X = BCK-part X

then X is BCK-algebra by BCIALG_1:14;

hence the carrier of X = BCK-part X by Th25; :: thesis: verum

for x, y being Element of X holds x \ (y \ x) = x ) implies the carrier of X = BCK-part X )

assume for X being BCI-algebra

for x, y being Element of X holds x \ (y \ x) = x ; :: thesis: the carrier of X = BCK-part X

then X is BCK-algebra by BCIALG_1:14;

hence the carrier of X = BCK-part X by Th25; :: thesis: verum